A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.

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A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod
pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a
total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends
of the rods as shown, each with a force of 6.80 Newtons, causing the whole
thing to spin.
(a) Find the total moment of inertia, I, of the sphere-rod combination.
(b) Find the angular acceleration of the system.
Transcribed Image Text:A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.
FORMULAS
s= r0,
1= lever arm
T = FI, where
v = ro,
Torque: t = F(sin0)r
a = ra
Equilibrium: Στ-0
Non-equilibrium:
Στ= Ια
Moments of Inertia for Various Rigid Objects of uniform composition: Point
mass: I= MR2
Moments of Inertia for Various Rigid Objects of Uniform Composition
Hoop or thin
cylindrical shell
1= MR
Solid sphere
R
Solid cylinder
or disk
Thin spherical
shell
-MR
2
MR
1=-
2
Long, thin rod
with rotation axis
through center
I MI?
Long, thin
rod with
rotation axis
through end
ML?
= r®,
1= lever arm
v = ro,
a = ra
Torque: t = F(sin0)r
T = Fl, where
%3D
Equilibrium: Στ-0
Non-equilibrium:
Στ-Ια
Transcribed Image Text:FORMULAS s= r0, 1= lever arm T = FI, where v = ro, Torque: t = F(sin0)r a = ra Equilibrium: Στ-0 Non-equilibrium: Στ= Ια Moments of Inertia for Various Rigid Objects of uniform composition: Point mass: I= MR2 Moments of Inertia for Various Rigid Objects of Uniform Composition Hoop or thin cylindrical shell 1= MR Solid sphere R Solid cylinder or disk Thin spherical shell -MR 2 MR 1=- 2 Long, thin rod with rotation axis through center I MI? Long, thin rod with rotation axis through end ML? = r®, 1= lever arm v = ro, a = ra Torque: t = F(sin0)r T = Fl, where %3D Equilibrium: Στ-0 Non-equilibrium: Στ-Ια
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